#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/data-structures/fenwick-trees/bit-for-offline-queries

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░██████████████████████████████████████████████████████████████████████████████████

#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/data-structures/fenwick-trees/bit-for-offline-queries

Repovive

BIT for Offline Queries - Fenwick Trees | Data Structures | Repovive

Repovive.

Data Structures19 sections · 729 units49h total

Open in Course

BIT for Offline Queries

Process in sorted order

Many problems become easier with offline processing: read all queries first, then answer in a strategic order.

Example: "For each query $(l, r, x)$ , count elements in range $[l, r]$ that are $\leq x$ ."

Online: hard (need persistent structures). Offline: sort queries by $x$ , sort elements by value. As you increase $x$ , add elements to BIT. Answer each query when all relevant elements are added.

# Sort queries by x value
# Sort array elements by value
# Process in order:
#   - Add elements with value <= current x
#   - Answer queries with current x

This converts a hard problem into simple BIT queries.